TAILIEUCHUNG - A decomposition of transferable utility games: Structure of transferable utility games

We define a decomposition of transferable utility games based on shifting the worth of the grand coalition so that the associated game has a nonempty core. We classify the set of all transferable utility games based on that decomposition and analyze their structure. | Turkish Journal of Mathematics Research Article Turk J Math (2015) 39 ¨ ITAK ˙ c TUB ⃝ doi: A decomposition of transferable utility games: structure of transferable utility games Ay¸se Mutlu DERYA∗ Department of Mathematics, Bilkent University, Bilkent, Ankara, Turkey Received: • Accepted: • Published Online: • Printed: Abstract: We define a decomposition of transferable utility games based on shifting the worth of the grand coalition so that the associated game has a nonempty core. We classify the set of all transferable utility games based on that decomposition and analyze their structure. Using the decomposition and the notion of minimal balanced collections, we give a set of necessary and sufficient conditions for a transferable utility game to have a singleton core. Key words: Transferable utility games, cooperative games, core, single-valued core, balanced collections 1. Introduction In cooperative game theory, given a set of players, players cooperate in order to optimize their payoffs. A transferable utility game (also called a cooperative game in characteristic function form with side payments) with player set N is a function that assigns a real number to each coalition. Many different solution concepts have been established to determine how the payoffs should be distributed between the players in the case of cooperation. [3, 7, 8, 9, 11] are only a few examples of remarkable works in the literature. One solution concept that has received a great deal of attention in the literature and is widely accepted as the major stability notion in cooperative game theory is the core, which is defined by Gillies [5]. The core of a transferable utility game is the set of all feasible outcomes upon which no coalition can improve. Yet, the core of a game can be empty. Shapley and Bondareva [2, 10] give a set of necessary and sufficient conditions for a .

• Toán học
• Transferable utility games
• Cooperative games
• Single valued core
• Balanced collections
• Nonempty core